{
 "metadata": {
  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2,
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1,y1,z1 = symbols('x_1,y_1,z_1')\n",
    "x2,y2,z2 = symbols('x_2,y_2,z_2')\n",
    "xa,ya,za = symbols('x_a,y_a,z_a')\n",
    "xb,yb,zb = symbols('x_b,y_b,z_b')\n",
    "vxa,vya,vza = symbols('v_x_a,v_y_a,v_z_a')\n",
    "vxb,vyb,vzb = symbols('v_x_b,v_y_b,v_z_b')\n",
    "t,t1,t2 = symbols('t,t_1,t_2')\n",
    "D = symbols('D')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x1 = xa + vxa*(t-t1)\n",
    "x2 = xb + vxb*(t-t2)\n",
    "y1 = ya + vya*(t-t1)\n",
    "y2 = yb + vyb*(t-t2)\n",
    "z1 = za + vza*(t-t1)\n",
    "z2 = zb + vzb*(t-t2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "   2                                               2                          \n- D  + (-vₓ ₐ⋅(t - t₁) + v_x_b⋅(t - t₂) - xₐ + x_b)  + (-v_y_a⋅(t - t₁) + v_y_\n\n                      2\nb⋅(t - t₂) - yₐ + y_b) ",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle - D^{2} + \\left(- v_{x a} \\left(t - t_{1}\\right) + v_{x b} \\left(t - t_{2}\\right) - x_{a} + x_{b}\\right)^{2} + \\left(- v_{y a} \\left(t - t_{1}\\right) + v_{y b} \\left(t - t_{2}\\right) - y_{a} + y_{b}\\right)^{2}$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "30.0000000000000",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle 30.0$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "30.0000000000000",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle 30.0$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "20 - t",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle 20 - t$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "-10.0000000000000",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle -10.0$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "-10.0000000000000",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle -10.0$"
     },
     "metadata": {}
    }
   ],
   "source": [
    "xr = x2 - x1\n",
    "yr = y2 - y1\n",
    "p1 = xr**2 + yr**2 - D**2\n",
    "display(p1)\n",
    "ans = solve(p1,t)\n",
    "sub = {xa:10,xb:20,ya:0,yb:0,t1:50,t2:0,vxa:1,vya:0,vxb:-1,vyb:0,D:0}\n",
    "t1_0 = ans[0].subs(sub)\n",
    "t2_0 = ans[1].subs(sub)\n",
    "display(t1_0.evalf(),t2_0.evalf())\n",
    "\n",
    "_x1 = x1.subs(sub).subs({t:t1_0})\n",
    "display(x2.subs(sub))\n",
    "_x2 = x2.subs(sub).subs({t:t1_0})\n",
    "display(_x1.evalf(),_x2.evalf())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "   2    2     2      2               2      2    2      2      2              \n- D  + t ⋅vₓ ₐ  - 2⋅t ⋅vₓ ₐ⋅v_x_b + t ⋅v_x_b  + t ⋅v_y_a  - 2⋅t ⋅v_y_a⋅v_y_b +\n\n  2      2              2                                   2                 \n t ⋅v_y_b  - 2⋅t⋅t₁⋅vₓ ₐ  + 2⋅t⋅t₁⋅vₓ ₐ⋅v_x_b - 2⋅t⋅t₁⋅v_y_a  + 2⋅t⋅t₁⋅v_y_a⋅v\n\n                                       2                                    2 \n_y_b + 2⋅t⋅t₂⋅vₓ ₐ⋅v_x_b - 2⋅t⋅t₂⋅v_x_b  + 2⋅t⋅t₂⋅v_y_a⋅v_y_b - 2⋅t⋅t₂⋅v_y_b  \n\n                                                                              \n+ 2⋅t⋅vₓ ₐ⋅xₐ - 2⋅t⋅vₓ ₐ⋅x_b - 2⋅t⋅v_x_b⋅xₐ + 2⋅t⋅v_x_b⋅x_b + 2⋅t⋅v_y_a⋅yₐ - 2\n\n                                                2     2     2      2          \n⋅t⋅v_y_a⋅y_b - 2⋅t⋅v_y_b⋅yₐ + 2⋅t⋅v_y_b⋅y_b + t₁ ⋅vₓ ₐ  + t₁ ⋅v_y_a  - 2⋅t₁⋅t₂\n\n                                                                              \n⋅vₓ ₐ⋅v_x_b - 2⋅t₁⋅t₂⋅v_y_a⋅v_y_b - 2⋅t₁⋅vₓ ₐ⋅xₐ + 2⋅t₁⋅vₓ ₐ⋅x_b - 2⋅t₁⋅v_y_a⋅\n\n                        2      2     2      2                                 \nyₐ + 2⋅t₁⋅v_y_a⋅y_b + t₂ ⋅v_x_b  + t₂ ⋅v_y_b  + 2⋅t₂⋅v_x_b⋅xₐ - 2⋅t₂⋅v_x_b⋅x_b\n\n                                      2                 2     2               \n + 2⋅t₂⋅v_y_b⋅yₐ - 2⋅t₂⋅v_y_b⋅y_b + xₐ  - 2⋅xₐ⋅x_b + x_b  + yₐ  - 2⋅yₐ⋅y_b + y\n\n  2\n_b ",
      "image/png": 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ymdnmyoAbO0Ogi4CtLHcRsXNDwBC4OQRueeXy5pR9sA6bbR5MYSbuVSJgzvJVqtU6ZQgYAoaAIWAIGAKGgCFQAoHDbsPQ3Tb7uF57EHjjlVDzr3fPHOzXEDAEDIEDIGBz5AGUZCLuEgEbO7tUy6ZCHdZZFmq8+dt8wktpPl3ENz+/3BRRY24IGAKGwD4QsDlyH3owKY6HgI2d4+msqsQPq1KvS/yVHGQ+WxQC3yPmI+Puw+Mh02JDwBAwBG4UAZsjb1Tx1u3FCNjYWQzhdRE4srPMqnL8b2LXpRnrjSFgCBgCyxCwOXIZftb6dhGwsXO7uu/t+dW84KcVZVaWnyu2bRi9qrZMQ8AQuGUEbI68Ze1b35cgYGNnCXrX0bbZsyxj4CW58HH5b5Tmn2/4R5s/995VycjWCz6U//XeZUW+I2N9BHy3ktH0uhXy9fkeXbeS/xBz5NFxrm+Jx+RwZL3a2DmmzZWW2q0se0NmQ3vzv99Ks1L7Tx3fKv1HzFjnfImCl+koa/6TnjpjZZSXDuKHk8/Lfd8pfV+afml6Xt5DYl0ai2uiZ3q9Jm22+3J03Xr5dz9HHh3nttXYWUDgyHq9xbET9GZxG4GwZxnH+GVcJCNhlRnn89c436d5sY6X6VqOckJZD6n5WdEgxGm/1/GVz5tPdKKl6D/T8Wqi2ljxIbEe69A1lJler0GL1fpw2DHr50NuzqvPkTaGqtnf0Qkfcvzc8Ng5ur1VkT84yzi/f8s4WDGOAyvKj7zRxPnf6mRoe8ZYWUxjUdrLxGrJG6VxknnMyKZ8to/UDGDUxSmH3+GwzuncgeuaXg+svMqiH3LMbjBH2hiqbIgHJX+48XPjY+egZlZX7DtPHqcYh/N+gF3XOcT4fxuoO1Y20GRWNttAkIu4CeoDDvOewxGx3jOee5HN9LoXTZSX46i6PdoceVScy1vcdVE8ol5veexcl/UV6s3o1zDkeH4QH7ZbPNCBE4wjioNKmgGAc/1OB6vMvWVq96PKkoPqQ59tDnzV4kPcXmnk4aXDIUddxXWDePMiIZhk9WtKKt+3q8da/dylfk2vUxY6Xr5XvY5Lvaz0VsZsKkrXMoa2suWt+Kbqt3Q9Gz+fEd167Ij/j1vbX8QfYJ7qYGsw76R9r4PwTnU28/3uzjJc/kootjUgqPtChs5xjv9QjLPIvl22W8RhrCyuN5V+Ldo4xPB5qyN2Sh/rHOA2A0y8iwf19Zawvhn9ml6boXJ14/bGdNsocu3ERjhvNUdtxXdttZ420iv9NIyHfbitsWn+NVH2wccl8P9wkPEH2XLL3vfNfL9BZ1lC8WLfzxIydlaVdRrbkzxYJjqsKL7Q8YPSvZ94Uz7OOSvVBGh1XyB8qTzuOK4t3ATWpfUretxkMKA+Ko297C0U06v6x/h57TvIOCG8VP79OXn+1fnqY6g0T9Hbu14Bu5huIaY+T+q3NM7wPUAohvOeMS6tW9Hb+xhaVa/YeWmMr2nsbI2N+LObAGc4DiyYusVaxSy4dMvjutXTvc6yBMeLZ6W4b/8vWzCGvPveMtFh4FJG4KIwFHB6Am0c6zedijgG7zp5VU49BkHmmAdKO6m8D5s/ld98fi9uNJT2fG4F66L6FXbgzQ1V96ZqCO6Tx/twelWHmrtuOuf7wb667p/wFMUYXgmhKE/1LVuvQUa1ZX75t46xeSZUDzGfnRx6YTnUaWKPfbEx6wmn6Lcozk2HMhO+/9c6hrbCuChf7FlH7txYfexgat5+So6flLED66IYQzA3+L7vcexsjc17b68BUrfwGvIUZ/lVgUhfLFqz7PyuS0yE3GfRFF84g54JK1e/97RDgKEyLkQMXu4UBoPK7ylUjDFB72fOo8BLiN2V7qi4XFJ8LvoPdeXThyJ7lkXrprBWf2voF1v5B7pJCZLhkHpV315J9l91sB2KwF02eYyJxtFTugbGjuHQTyWeWXoNsnlZep9chTpLYtEvPma9PJP6LY2z6M1afVS7qx1DpTFOtbVKfLPGkJeh2tgBC/GoMX4mx47nXXRuVF+yx4/a7HLsSK6i2KTafagn/s01zOdhu2FVOVQrEvu+Ztv5XcxdRHAEv1TcKFRp98hXMXep31Bf6XDBJs2n5QB6rIxmOYG7iL883bjdk/jkyGn17TBYS1YMl4nhqdLNHZ7Sv+totj8o/Uh1cOLCm8To6yfld1d+J/WrNpM8VQeZ4PnM13+q9MXWBOWtFiRHLb0yJt9ndGQSY2hJXvaGEVihRnfwcXpUmdOb4mJ6Fe1JnuK3O716uWvpFvI5+k3SLUTHgnDOXn0co1eqTHLVwrkoxpJzco4CE9VLHT9Un9RtCl/V2d0Ykkx70GsSxlSaCurP7sbPQozp8qT9UUl8Sl43INkE0WZcEcIuA/gxhojviQk+L8XfODdY+PswtBfj4Ax1vXkM/KOv55bGozaUPU4oC01SYxz01p2G5IPXL6kE9lzvgFjzhwas6D9XHIwWe/km4OzzcZJxjnkiwA0VAyrYjpJNSNHvJE9RY1Dh0IW99WzRYfBsEtTvamMITHU0E4U6yIWfG8rWOIk6Pomx2qKf3xSjW8YxumP8o1f6ctI5+i6mV9Gb5Cl+u9Krx6Gabj39HP1O6haaiQGsdzOvyj6q4SzapTGenKMyxw8qS9HtJF/R2dUY2pFeUzGmXkrYzfgpgDH9nbQ/8Zmcw3Psnro6WHgDSwLXtpPO40U2Xj5srn9K51yXILc43EFBjAGIDffsI2K/cghcQOOtD9SLV5vYjhC8/7GyQC81xgEIwAX5WNUMvMijPEys3A25oPy5q52BRNVY8h0Kay8vf/wC3vFqP+fxSidOKvYTO2/8q2Jj4BGwo/rN4MnNGw5e4EHcOPARv+pJL/MqY0i8sHtuHsceJY1i7AFBP2FCYvIJ26teKj/osZheM3juRq/ILCxWHbPiN6XfFN0iNxc1Qu9TA88HvT9TmvH8VAe6D+NJp+sF8V0NZ9/3sTE0irGXtfS8CNil+O5mDO1Mr5MYU0EyT/oXqsM43cX4KYRxEjaqVPq6AdYcfPUCPD/CQ4cLXhfdd9VyrkuB1KL4oW/NRZ6Jiv1E8cFk0gitNKtO3AVQ54XieP/wWJmqpwfRhRYbvtm4Dy8mc/LiMHl3rTYAn7oqFtOumT4U1sIwOMjc7TU3K0pzYQ3OFXihJ/oWAsbfbNcJmcRel4P6zeCJY8zFJQScx+D8hby14lX0KmwYp0wUXysdj81WP6cwprLqxO8ENPpSfoxpMb1m8NyTXhF7Fd16fCb1m6jbydUf8UPnjJddPJmRHKvgLPwWYywaxedF9f80pdsMvnsaQ7vRawrG1FGY9C9UZ0/jpwTGk/YHMLLBotcNkcRPgCZ4vhJ9fA1u2lkI4/qDzxn7HspK9zeoXCLcQUSCjK1QNXxUj4mVO9aLMFZ2UTkhQ/TcUnxfVZUx2dW4q+9jVzRPsh8K66jz3EXHTx0w7DeUq0/clBBiRxU74YU0V6a45djpfFC/jtL5Z5CnrwPteHX7hc5f+rJVI/Wnul7Fw13kFbsxqBh84rv8Vp9VnoLxydMhdk6yYp4Y4QzU0utJtJGduMXTd2A3evUyVtet55OsX+E2pdvYLsAz3NhyEQo3Q9jRLp7MrIWz+l4SY8QenKPEK3v8eBymdDvKl0KF3Ywh4VB9/OToFXBUfxBjTyvFv9jN+JHMizEGF8IYNuca51/V653DlZ9l96p/L4otfSgP57jrIDvGufTP0i7/fbicxPoUBFaVu/rEnqBYjlsMH+m08MdR5m4vODotTJTPIKIOzjNPIJbg1ctTdAmNcy4e3IGyWt07wFzt8Z9WH8arrl+qfnGR52aFSZytUWDMBOPwUZwVoKfjb9/oe8VOl/7cTVwqb2Hiec7WawpPz7+kXj3JfUdgIwlL6jdl9af06mPLXvaGeGmMo/71zlHi18JD5yXnRdj38vVy3cwYKq1X0Uv1L0qOn5atRLa1qyRY61j1utEFQPxbWOm89LjqsnTnd725hTMBWCS5AHOhBWwuCq2/stb5nABIxVY7UwSQ7L1bC1LarlGnItZsg/lB9NnWwh7x2Lmia+Sx54hyJnHqc+fNX5TPDSk82aoDjyeK3YrrHGZqu2u9qk/g+sjHTRcld+uOvCmYTqAj9phzk+FWHZXm0f0THW90hFBSrzk8i+g1dOIAcWn9ui5Lp8yRJ8VuvCp2Tw08HthTsSczon1rYwgYU+ao0vNiKt9bGUNVxo5AHvQvUIBCsfFzgLFz7vH52r72dSPwjuOS16WY7mD6wadPnwYL914gA8NJcn8ooDSOOC/3PQhyK80dEHs7uVPE8BlUOFRcMOKVF2VZGEJAWDEpPAZH6ijGuWKLRTUMRXt1nvTNgiFwdAQ0dlic+I/iL3Swv/2ZYveYlnMdOHgnxcyfbu+70tw0MZfOvuGE5i0FYbXJHLUV31vSLX0VzlP+hY2fGzKKVVaWK+K51V19xS7tkvRbSfVOx4+aQLgpwXGu5ih7BLbg6VlbZAgcGgFbwV9HfVvNUVvxXQfV/XBJ8S9uZfV+P1rZSJLDrizLWdvkrn4jPW3KVlg/lwCPdYA52x3cylRNobbgWbM/RtsQMASuC4Gt5qit+F6X9sZ7I4zNvxiH6OZKj+ws86mUdzLqsNrJHV7SG6E3p2XrsCFgCBgChoAhYAgkISBfwvyLJKRup9KRneXVVztvxyysp4aAIWAIGAKGwG0iIGfZ/IvbVP1grw/rLA/2yAoMAUPAEDAEDAFDwBAwBAyBQggc/QW/QjAYGUPAEDAEDAFDwBAwBJYhoFVp9ju/9lT4Mg2BPwO6PyfzfkvTy+OeX7uGvDVo5vbMnOVcxKy+IWAIGAKGgCFgCBgC/Qjw/lTz/Xul+S8IPlv7ZX/1ydzS9CYZLqxQQ94aNLO6+TCrtlU2BAwBQ8AQMAQMAUPAEBhC4JUcZD6xGgLfOue/HdwfBIXMjLg0vQzWs6rWkLcGzazOmbOcBZdVNgQMAUPAEDAEDAFDYBABVpXjf8YcrJhYUJpeItvZ1WrIW4NmVgftBb8suKyyIWAIGAKGgCFgCBgCaQhoRZmV5eeK527DaDEqTa9FvMJJDXlr0JzqerNnWczZiB7+bOIbpfkXKP7T/s8pIlY+jIDhOozN3BLDdC5y/e0Mz35cluQapkvQu2xreF5iMjfHsJyLXH47Yc3WCz5DV+Q/IErTy+9RXosa8tagmdIrt7Is5jjKbKD+LjRSmruhf+r4Vuk/Qj6xznnbkw3rlP1FnoVLBISN4XoJy6Icw3QRfBeNDc8LSBZnGKaLIWwRMDxbcCw6MSwXwXfRWHgO+kIea17u+07pWV/CiBmWphfTnptes//IuCUGYc8yjvHLGDAJxSozCuafbLqBzetsWDdHuYtM+9xwbePReyY7eqbjVW/hZaZheolJK8fwbMGxxYnZaFnUDc8RPG28j4CTUZSJY6Dc6wuJVlgoY0HxXsdXPi+0y4pL0+tjLh451+FAYpX+w2wNDEKn+uLgLNPhvyUMd0lxYEX5kRcyzv9WJ7Y9I0akP2249uPSzcXuurbXrRPODdOAxHBseA5js0aJ2WhZlA3PcTxtvI/jk1qag2OgeeELeX+JFeU3SuMksxWDF9TY2podStMbEWCX/UfeFTEYhOfOl+AUo9T7gZqAGAcmr9/iDEv3ImC49sKyKNMwXQTfRWPD8wKSxRmG6WIIWwQMzxYci04My0XwXTTu84XYoorPRNwE+Vc4zHNCaXpzZBhqs0b/4b05BqNfw5ByP0hItls80AEoKBsjIM2gw7l+p7IfdZDPo3Te+PxAnmIXlIYOLwtWcbAj3vB7qoMtJTwG+V4HARmr8D6Tz/v1eOwW17XxFD9egACPxmbyEHV3nru31bVwvUE8++Yc5qO3wqJ5DyPXpkrXlyxHstHdY7pnPCXb2PWwqG2K11XPn2thmYqj6o36QqnzxkS/qvpMfTLeev/7MInzwjaMOM+lBRyPDnA43RcydP6HDi48PF44Kc1eHFQmEJ8AACAASURBVDauBwfntU//ruLX1InCY6WD4xplF0vyciIOO7K80/FWxzOdIzsTE3vedhEk0xFwPQyeKPUgmCLqIXA9EJ5jc84L4Y0TsYtgmJZVwwHwNNssp/JdYSnbm/KFUns+1q/aPlOqjBf1brX/dxdIfM7gxb6fBUxwhkPJ0B4dnFQC5d0X/1jpZcW3eJB8rGZ3nWEuks7JV4zRNeWqj7OKM/1RaWRdO2yGa0rfc/FcG7wBfpthijw1cE2hOYBFiexN8UzpgPDhRn5szmFs8/RrL+GqMN3YPtHppniO9d9sM+9aXwrLMTqVJgHmmFnvbiXYSDWfqSAWN9X/XmdZimT1mLunvj02PILobmnA8Qx5rOi86SjkXufhwtYpWnz6Xrxj59wpMOQpbj2G1fmfvixucyGE6rAi/W8dxKmBlfbBwaOyTXFFNh30e6zvWXimAkM933/spxu4oaG8z96QuaXDuLGnuamtSobiuKbQ9H2/Ojxj/Y6kP6r/Y3MOuHTnoRFy5yLRvLpxP9npzxWSMU2xT8heK54T/U/G8TP00ynx5PpxdeO9FJYTdBqAC+KILsIc1NBPTEzZSDWfyfo/b46/6ypWQLpPeCm+cFyUx4WEFR22WjRB+Sj2pBjjoc7PnEeBlwe7K9RR8fyk6HadU2QIq8pDhKnzj6FC8kWXPhX5kLintxdcR/s+E0+6OBlE+8KmaKT8WXvu1G4vmNKNGrhO0bxmPMF0MEj3g3OOynh6xDyUvbLs6V7juB/EMhTMwHTUPqF75Xj29n8GjkEFo7HoXvN4L4VlL50Y2BI4igbzy4UvFPj4chYOf1D6Yj5R3uD85WnU9JkW29HB+w/2FzoJuhuK7+ICAYDT8qXiBkylMYiTYlYjv/Hp5iKkfD4t5xSvMlYA/4rOqU54co7Ovyrnz04IvETCFgn4YXzs6XSrnordufLCW5DQ+CmUK30RVMZAITR3e57OSbGTUXG4kD5TmvpsD3kZymlcOoj2LnDN7bvHBzgG8aRQ9bJ1RbslQTx3gSl9kCxZNqX6u7PTNfD0/Qarp0o3TwuU/l0HT4SaoPNUm4LOn6rvxrcnAL5827S5kc6g18iwNCGe1W1UPOjr6piKb5bNL8WS9nvCM7H/ZpsJtlkKy0Q6JUwRGoO+kJcjzPHMY2MBG5n0mcYIbFR2c/1/GID2CuYi1l2VZcL/6Ou19qioLmWPAw3FONbNBYp8X+cX0gSd4yj/ppiVZtriAMMT8JmAqYOB4SRTxio1zjntghxKnuupnAttMEzn5Os83mbAJvruhZTysB+b7SHNnmbolgziTZ92gavkAKfBvktWbnyy8KSNaE7qSnWKhZ1hSr+K4zpFsxiYIrQWnmLFS8GM++eK3UXE83YTb+iTL0u1KeaceLxDhnmqdUOv81R6tF8cfL+qj3sJugmm4jtq84sB7BDYG56J/TfbTBjvpbBMpNOxrNmng76QbJWbd+a57rzUx2zSZ+prtIO8m+v/HaBLsSiMFybY+8m+qBBwZuPHAc3gVz0udnzuq1l11DmOMpOoC54uF4y4Dis+wYigEbZ0sLobHG2cV2QJ59Cj3T2JKMCLg8/SQQtnuqmjPMq6e6VRMk54qEfculjrvEgQj73hOtX3OXim6upaMaVfNXCdonkoPP1Y4CP92Fi8ksL5+05ncmyKuYR5ygVPH5rN0zGlc+idCS34XWvcb4zpKvaJGnaKZ0r/zTbTxnspLFPoLBjZraZTvlCr8shJis/EGKjyNH5Erqmi1fqvvjOfh0XHwSeSqocPyFzPwgjpyd0IqpMc7nxNHGU67/aAdlrHDisrwDiaYa9oax+y8nFaKUdgvhN4Io84BJ3H+5kBwZUrP+YDfQw/BOo1K0Uh0+dBj3J4sT+IlVEcfgCLN9FThYBjjHwhsHclOO8hr1S8N1yn+g7GuXim6upaMaVfNXCdonkoPDUm3RhjjErw+Ob5qc7DDXPoU45NMX+8FV3G9H91sLWLEM8XOfTOrZf9rjLuN8Z0LftEE3vEM6X/Zptp470Ulil0lo3sz63R7aAv9LnaeEpjOMVnCk/jWWRgLMCXJ0r4ODiR5OMccv6d0qxsk8/5Gx01wmr9l/D0FZw+6eDpNwun9A99u0C+ElX775xlMcJhnAyqxwUvdmIv2qhOvKJzUR4yVI/OnhQ7J1kxq9RB6RTFDiw8f1U5gJwU30dxi5/KuBDHF2OqxgEa8UrWC52/jCuUSkuW3eDq+zTad49rMp6q7/Qh2pO6umJM6VpRXD1WozQPjCfjPn56xY1uM6Hn2pS32Xi1AaeZi0Vwzm/BRlfF1NveKvYJL+ly7Xl0FM/U/pttOqRWwTJVJ77e4sjPL6O+UCoT0Wpdc3valXwa30M+P2ut/osPi7gpTySZ91N2I+R31rd4OLvljIZ0XMffvun3iuPVZGcwKr9XPocLOmewcUHl4vfCl7uymT+NYydarDjxqbQx53omm/WaSf5JXL00RfvudVFCVy2dr4fcMKcMTCFSFFcv1RKau8Ozg/RHzoUx45qVgmYeULolu84Hx7/KWGFhNcEFpR8pwZiOne9kemcqh/1dDVOP0BL7PALIg3im9H9l22zZ+A7BrY5lik4ScNkljrKl7tN499RM+c28qb4x77HqHAJza/x0LeSPxbvrv/oYtuzhH8Z+WveJZIn+j2FzuhstLV/IoMH7p2Pu0avSPGJ4oqO5wCnNShHL7lwIacOSP3dxbmuH4iUB2nx1A1pPFBe5O1wiUIG2ObiW7vtiXUkHuYO6AGSTJFIxhVANm5pNc6d4BsAZy2yXco/MlP4zFERxqk1xQYhXqd/qnBd340kVsqn0qHvEsBWmpeeSvWCfiudY/1ezzSsZ76WwHKMzal87x/Ek+Vg4IHZzpuLsp/FjAIjeHq/DQeTBJxSS+5Gv1NzA6xy/7mI3QiA2J37w6dOnOe2sjSFgCBgCWQj4Se2xYjepKeaGmQktXjlJpql2z1WZx3QE9ipDa88TvhO05I/6y4XCMC0Eaik8zTadU1fENo+KpZcb5z28R5FtpWrL/PYfxV/oYKvBM8VuWxLnOrixOynmif3XilmJxbFkMQKHEYd61vyqtouC+DI/L+p/EEC0WNwM+7G5EeXdtAdRefX+r72yHPpmsSFgCNweAqz8vtPxoyY6JjycvNkTudp2V5BvD1G93GiYFlV7ETzNNp1ObhJL6R4Hl20DzHE4qzz9+qC49UEE5aWE1Cecu3l6Vrj/AaOppz3V+28ry0EVFhsChkBVBDSJstLwWAcrTmyBcqsiVZleOXHDtKyCDc9yeBqW5bC8ZUqyoyJPKJZiaM7yUgStvSFgCBgChoAhYAgYAoZAcQTkLPPi4jvF4YkkWzuSvpBTUhhzlkuiabQMAUPAEDAEDAFDwBAwBIogIMd4F08kzVkuok4jYggYAoaAIWAIGAKGgCFwjQjYC37XqFXrkyFgCBgChoAhYAgYAishoBVg9ha/9uzCV4peKv9+rgg1aM6VxZzluchZO0PAEDAEDAFDwBAwBAwBEGAvMV8BcUFpvgLCJ+xmfzpPbWvQdPLl/jzMbWD1DQFDwBAwBAwBQ8AQMAQMgQiBV3KQ+VxeCHwXmk/nuT9TCZmZcQ2amSKcq5uzPAs2a2QIGAKGgCFgCBgChoAh4BFgVfl9YTRq0Jwlor3gNws2a2QIGAKGgCFgCBgChoAh0IeAVpRZWX6ueMk2jBbpGjRbDEZOmj3LEoIN2eFPAr5Rmn+O+Zfy3f+Qj9CwooMiYDo/qOJmim36ngncCs1MNyuAnMnCdJIJWOXqpo/KABckL12x9YJPvhX7HnINmjlddivL3gjZSM1fBrqgNHcF/9TxrdJ/nHPPvzrnrUf33+NK/xWXpaZL0EjlZfUuERD+3ByZzi+hucqcLfR9lUBW6JTppgKoC0maThYCWLi56aMwoAvJSR+DPqDXFS/3faf07C9hxCLWoBnTT0mHPcs4xi/jBhKOVWY6yr+ndAObuNm4PctR9sRK0OjKZefpCJjO07G6hppb6PsacEvug+bDZzpeJTf4XNF08xmLvaRMJxU0YWOkAqgzSC7QQ+DW67+JbliEY5H1XsdXPi+0y45r0OwTQnxG5+/gLNPxv1WZu4U4sKL8qKez3yp/6faMEjRiWS2dh4DpPA+vo9feQt9HxyxXfubP7hyaQsN0k4LSunVMJ3XwtjFSB9dcqnP1EPhc+G/eT2RF+Y3SOMlsxeAFPbb0zgo1aI4IMorJnW+IU0zn7gcIQSQOTCS/xRkz0iVozGBrTTwCpvPbMoUt9H1bCM/vrelmPna1WppOaiE7j67pYx5utVr1+W9szcVXJG6C/Mrm28tNZnqiBs107lHN0a9hqJMfVJftFg90AA6dBgzSGC/O9TuV/ah4MpSgARPRQQYed/KW5YeYv9LIzIuJS515kWmHrfi2pah75vEznQtm03f+GA/WuRV2EV9EeaqD7WU8GvxeB4H5qvjcAGHR5YUWxk7SfEibsSA6RedfeInmJnNnhzenq+oGhiXCtehkwg6wkbeq07zDVAI7aIimjZEeMNfWxxw9qM1iH9DbwGZzUA/0TdYUJndNzU5CDVlC5yLjvpChc5zjPzzBZ4pZhs8KJWh4hq9FC4eYgfdWR3xxeqxzLow1Lohb8VV36gfhaTpvw2z6buORc7YVds0/PsmeeUGZ+QEHmfmCR4TsRa0xN4hsuVBjLHrpttIL7A+tmyvTyZgdvJCuuLbuOpg+1lWP8F7sA3qJx2yvpv+2CLBBZ1lUebHvZwEUO6Iwu9irQiZBdbljYKD9oPTYJ0N6afj2r6GlgKNOaP23uOqQ/86VnGXpvmTIShKrFkVDab6ih2PKhfyj0tk3HkU795mY6dxjYfrufydBuEyO8dLYfTbP8ZT48rQJZzgOXPTdDb9iJuJueVx3T+niY3ErvQBqrm5U/ybmxy10ksCT6xGO0d7DVYyRHH3sZFz0+m8pxpLQ1yr+W4psU3V6nWV1iBUYVpH79pqwFH+xMuOVSBmBC+pY6KWhBs3KA429HOxZiT9qjXMZ+OOYv6FuFO6VDs50lL04WZSv+vCnDhz9rrPfK6jqgum/dUxhG7fn0y1JL2Kqnuk8Ru58E1PMztCDjlvRd9Gx0lbL6Nl7j3Go5Cb1kKe4yGNl0WGshLku8CLGGT+pvG/eRP9J/D39GvPvVnoBlizdCINbGS9b6GSKJ7bdva6iw+TgbdjGSBpiyfqYMS5qzFVD/ltKb6f6Wst/a2Sba5t3DQWfECH36SPFFxO+8nDUWNn9vacdTtmfqjP6+GaMhtq/UvmvOsJdLatA5PHyoXP6FAPmSTEKQ56fOY8Cdbur4VHxvGQlvvThHykSef5jq/UpZHrriLbpvIOM6XvRGN9qjHZvDBlfYVW5o+H5p7KNi7kRaspn7lu0Z1k0qo1F0d5ELx6bObq5+vlxC52M8VQZK/pcV8M1GPVlB9GxMZKI2gx95IyLonqQrNjGkA9I2Wvf7aGdAUXnIG+vWU/o59rmXaxPEWGy/zImprTrtGJWxb6hvtLNQFKaT8s5AChLCGM0UOz7BBpUYZXmrx7eT+L2KmffIoHVaZxveKBUVrHdqq5id6688OYlNH4K5UrHoQhf0Q6T0jOlMf6nOlpbTmKmtdLifVU691iC7VOlm5U8pX/XwUqjC0qn6nxS36KF/kZ5qs4t6dujvNkYPXmdIEd4OkAeOie+Jyb4POaFlLHv2tT6kSxrjEXEn7RpKkme0nMnZKHLeCEM6kZ1bm28TOrE4zY6zwCq6uXMbSxwNeNBzdEN38dtbm4y6MG+apAsuxkjkmVy3geMDPywgVF9iNbW42LMf0vZGRDsY9LeQ8WxWHiAV/IT2zFaU2UPQwWvBByM7koMxvnR12vtVVFdyh4HGonxIA3RY490PHBxbHGIm4Eb8cCJb+V7eX4JdXTOZP+bYlaakRMHmP6hcIzupHMmFi6UlLFKzY0A7UKflWyFInxFkYGGksO+cLaOcNFeLai/YHBVOld/+Bg6+uY/6dHtyffTDXJ/nqPzSX2L5iRP1bklfQMzYRI76abIGEXXOrghAmeCW1HRubshPmedeLGkmV+UzrEDT6JOJFnWGot0YDW9wAycdWTpRs1ubbxM6kSYTM4zYK16qdczeMbjQ6funaTWYlgGPdpXC+rbrsaIOrq6PsRz63Ex6L9JtlfSUZh/sQP8GZ60OV+LjCik2HtUfTQJz8bvG625oPCOtuoMgrNZnn1y7HEJ4bES8baGZnCpHoMSIJrVgdBoIk6iIboAjDM+tPUAR7lRjOpDF8cvloc75DAZIG/YPvJS+cHRRqH0O5zr1N1Z35PoCaX4YnQ46IEPcePQ9fAtmiW+V6dz3yc+iI5dxE8dOH8fAZij81F9Z/C8JX0HqEex85VKjVF0zMFXLxjrH3WEsXXyNtF9lyHHDkSuTvA2tNb8SyfW1Av85ujm1sbLqE68jZSe27g2co13wY8RdOVuNH22jREB4fFv/IsN9bHpuBAUY/4bdhNfZ70J9Uaj9h5aCOfRp1sqx09kvn+mNLb7VAf+XTP367xIuPNUmKgBwe2X61CmUyGwKouDF/bVzdkbPElD9JGFQfr1UKeV7z4FpZh6fI/0RB5xCDqP9zMDpCtXftwn+oIBhkC95s46ZIYYHjrAYClfHGNohMBNQXDsQ17N+Op0Lp04/BQzaOObJgZQuFEC02Sdi9aovjN43pK+wfg0hZ2vU2qMMmahxfiFN1/kYTWTm39W2j4qHdsE1ZLtgMoVw5pj8SQcRm2afqpOKb1Abo5ubmq8TOlE5cXnNumF6+Fb0eY69F8d4UX6+PpnY6THv9hQH1uPi0H/TZjEc4bMyd109e4MUN2UOSg8dYQGcyR+F6v5zOc4yYwJ5ntitytBZbTBnuMbPp0uD3eQEIOh1dsWB9VDqNixbJWnnEzRULlzlBU7PooBJV59atioLAkQT+Ok2DnJilkRRwHckRDcRHROuv7xkqErU3xxh6K8RXw9H+jHd2EvdP7Sl1WP1Idr1jk2Ez8hYUC9AVT1O1vnifoe5AlfhZvR97m7599E7NAL+BHPGqNqxzhtjUvl4Rx3HWTYwCfbDlzDCj+SZbWxGMQXzxZWIb8bq94ivUBPNLJ042W4ufGSqJPBeUbts2za64W9oy7oHCcj7AE95dLzZKpEkmWvY2Q1fXhgtx4XST6g9AUuz3UM6k11puag2O+j32HBK94ZgJ+4yhP6h2K0myDwcJRxcnjcxPYPAAfQjzqyArR0/O0bfa84Xk12SlL5vfI5XPD8wp3KC18eipNitZnk6wk1DrracPfOp5V6L+xJjA9aCbwkehGddyBwNiP66POR4uCEFdd5xLeXpy83fUdAkUT3OlYfo553DTto0ex09zCnW+olAsnGSwRGJ9k7z0hvLfvTOdfP3uuZynAwWKFzQelHSnAdenPOaW5yoOnCGL1QJyFuyZhQ/whVVtGHB6LUuKimB9mJW/CUvIM7A1KUKjrxSjV27J54KN9dyz0NVtrjc5zzBiNfJzUaxeQulcpUPQ8QTiid4iKIA9T6K+opGipn8D7ycVNdtJxz22SkJTBg9iIzAbg7EqVZon+io5kQlObOmkcC8KYNjxm4W3FbOxTnhhy+vD0KnyeK3Up6LrMt60tmBsWedB7gQIc8hken6DceTNQprXNopvA0fYPU55AzVkqO0SBBUTuQvcWPrwOPVeJCYzHIurVekAPd2HgJGvkcp8wzKWOF63T89O2tznmU3V2wsTHyGfu+1Bb6WDwuas1Vfh5CPufPKOaGLV4h7sNwNM/TOCl213HF+JfBIcZffB8RmP2EXjRH5+8Hnz59ivhY0hA4NgIyeAbP4zCYFHOjxLaa+C61aCe34Fm0A0bMEDAEdo9AyXlGtHhEzmIHgb3K8f8buEz7GUfA9NHGR3iEp8TcQITAYho3b6zaJgdP6z+Kv9DB9qBnit2WDs51OB6KWWx0K9hKszD6neIqC4/FVpaTUbCKhkBdBFgheafjRw0aVk9wnKs5yr4rW/D0rC0yBAyBG0Gg2DyjObG7gnwjEBbtpumjDedWOwMWr7S3u9F/ZivL/bhY7kER0EWAFZPHOlhhZntLfJdbpVdb8KzSESNqCBgCu0XA5pl9qcb0sS991JZm0lmWQeB0vPaChMc2i75jV4NmbaCMviFgCBgChsB1ImDXpGPrdc/627Nsx9Z6eenHdJWyDYMl7uYFO6V5KYDl9vBNxjkS16A5Rw5rYwgYAoaAIWAI2DXp2DawZ/3tWbZja7289IO6epjA65UcZPZ+hsBma95G5C3HuaEGzbmyWDtDwBAwBAyB20bArknH1v+e9bdn2Y6t9fLSD+oqxVlmVTn+NEcJ8WrQLCGX0TAEDAFDwBC4PQTsmnRsne9Zf3uW7dhaLy/9oK4m9yx3ZdGKMivLzxUv2YbRIluDZouBnRgChoAhYAgYAokI2DUpEaidVtuz/vYs207VuZlYsa5S9iw3gqohWy9G/8KwqZyYqEEzkXVTTTLw4mL4agL/CMNH+fk2oPsIdlPREsURMOyLQ5pE0HBPgql4JcO9OKTFCUpHxa9zQ0KaPQwhMz9/Tf3lSrmWbGZXuZq5rN/VVWtlWYV8+YKX975VOvxDiqPiweflPj76nPWBaUeg56cGzR42o1leBjZ1809FLijN6jn/9gcOrX910fkgRufW9puKgLDkJsWwTwWsUD3DvRCQmWQM90zANqjudVT0OjfUjVx7GKJj+Z8RWFN/n7mmpdaSzewqTR9jtfp01d2zzIt88V8JOnoR+DiP/HXhVz5vjN9oWQ2aMBRd/umFf3JJDTjGL+PKas8qMzcEv8b5Pt2LUU89y5pGwLCfxiipRqbdG+5JqBavZLgvgDTTxrM5iX64eS92nZsQItceJsjtu3jv+qsp38q2ddV2VVNPjKAhXXWdZf4msLX1wDfkTvuN0jjJPKJiEzRbFWaFGjQjQVj55UgNOL9/S6ZuG1aUH3lZY1oXGMWFls5CwLDPgmu0co7dG+6jUFYrNNyXQZtj41mcKl+ThmTJtYchOkfJ37v+qsi3gW1du11V0RODaExXd51RBsjdv8Es+ReGgV0NmoF2boxTzE3A/UBDFBOHPozickunI2DYp2NVsqbhXhLNdFqGezpWa9fc4pqUaw9rY3IkflvoLxWftWUzu0rVzGW9QV3dyUnE+WOlGKeQx1A4jmw/eKf4Rx1fKD0ZVI/2bH/gKxkfaBsaKf1BaV6Yc4644iSaoX3NWLI0e5U7fNx3pFX+p45RjDrtBk9FJxmjQSKZBRFPWj7VwZYT9Py9DgJ67t4gnUsq/4rvatjTlQiLSRst0fWIH+R2g/2auEcYrI15Hz/G39uR/pdQ+yCNEb6HnmsmdLwZ5pFc6GR0/Knu6tekFHsIxpTTl9AmJa5FN4X3VJ0c2VR3Vf1Fsk3OMxvINnldBfucPkzpKpTXoBloz41zZFLdQTt6qMI/dAAuWy1OSrNfi5f4Gmc3UcjXvs3vqv+60+axzoNz1ina36n6wcULh9J9IUPnR8aIF+i46UGf73S81fFM5/SNCxn7m3YTJFct7Onj2jZ6GOwr4r425mP8XsgG+JrPbsKV4L5XzA8z/oJBdu0h5Cuu1ZdadCPRZyf3LNtebb4X7AG7qtGHGjR7+5SRWUSmu4jh7L24UgSOJY4YATqtL2nonNVM7uyPElhZ/1n96t4w9GKkejid4QYBLAgvlX9/TrqbkKIYiTZOJY7vR6WR6yIon5X+rjOMs+BuAhRzE9MtV9amoTj29EZYrIp/LvaqP6nPylopjvsGmE/pmHHCI8o9hUPjnqDjBvM1bVy8jjj3YZcX9lCrL7l0TX/naUM4HH6eqdGHHJpr2VKOTFMXhdhZZqvB3MfxOGyhLas3bzqMcRrfdfIWnYofK+HI3A04gCeVs7WkG9hSMfSIwtX1dFlJ7ms/hBF3wE19T4O9LzyiCaEoRuJBX7gp6d6YBH7E732dkOec/ZCneBSL0KgvVltuEP6tgzg18MSi9QJp3FBl6LQG9rBZG/8s7MFFx5Q+Tx6jonbvadbAfW3Mp/iBW3duwjZGg/ApbuswvBLckzFXf9e08azxN2oAPYU1bGLEHmr1JYvutejP47xkDk22+R7TGc1a0a5q9CGZZootFdATWCfLNKoYFd5RwSuIuyW2ULSCL5taNcUZhg4GyIXlZ86jwD7o7iptVNxOqu7kKpvqNM5p3Fr5rJzy+btkfqG92rhPzvXRVh796sVI+a9U/quOsGrFai159Ns5h4qLYuRlBu9/+PRFFHhHBdQPq8pRdn7S9+fr/Jb9LUSvGvZw9PISF7FR34tB/MWne1OQgv0gvYCa6Ba1e9Grhrtor2rzY/xUxpzCGA5jNEA6GXu6xWwdhqJ5Fbh7bOjPxbhSXh/mq9i4eM8Zf5O2ECqIPrZdzCZEb8weqvRlJka71J/6MukzRLpbNId63Z8Up9p8YD0Ze9rV7apGH2bQHLUl0VukJ8DOkUl1R23ozmuPf62DcHMhUZrPpjEhpKyaejInVir/8u1CHvGT+GQqrfZ/6phcZZuik1MufjjZXypuFKQ0zvFJMbKMYUSb99RNCEkYiSd/ikJgdRrnGx5c7NEHGIcL0TOlMbqnOlpbP3TeBF+H8/AE4KQ86BGjZxd8HvzCW6Ho7iflj61gnxvP/BXttbBHwtXxV//QD2EQe9XJ0ueZ3LLfFXGfxNxjBAZPlaa+C0r/rsNtM1KcihHtmUMau9Y5OuAb8Y3jobQbT8pfzdbF6yS+a9n7mrhPYq5+p+oPmIoF8Z0cf8WYzSCUYA8N1dS+qF6WbafQVZ3d6k+yre4zSCmTNt8oboOEMJmaZ5AqqQ+ilWNPkzQ3sKUUmUZt6KHXoXs8H/TpQX7sz1/pPEw2ZOFIsXLLwOkGnMvmYkShp/VLt2LCk8DiUQAAB41JREFUOTzntEsg3a7i+8JFurvqirF99LUHMVI79jfHF2YcWxzaFhaeziRGaoej/JtiVsfRA84qsn2jI+AOPjiwYW8121zQjQuqz80OjkbQnbsJ0Hns9LLxvZFbaQYEjgP8eDrAzROyBAyULBvEh/6shT3CV8cfHHVkYS+5RvWJ4CXDyrhPYq6+8WIx9v4c/OirlxGbDyEVI/jFdk57xm9rMUDnq9o6Qvg+rWXva+I+ibm6n6o/oJodhPGc8Teb35KGU/Ywpy+0kUyjtj2HrmjuXX/It4rP4HWeYvO+6rrRlF1F0kz2IcWeInokJ2mqziq2FMmVIhPVB23ozhNrCHlgcIbDKljOqinOIcxcEA3ocmEItE5KUx4cJLx9F5Q/ZwUpNJ8diy8y8lIFezbZMxsCTmq8fWQMo9DmJBr0DSd76FHKJEZqywpYuNgz8YXtMawcBweciz9O7b1iAnHXsQBrPtkHDRzeUPekPMq6+8hxtsEh8NCpk6VpR0apID5rY4/oa+APtrnYT+mzFOzofm3cRzH38vCnR2AWP5ni/H3U8VSMGDuMXxc8XWi5G0afvaqtw9P3czdzjZenFO4pmKfqz6todoSuOXLmPvTDPIldrPKkIcUeVIdrSW5fUmx7Dka71Z9w4rqL/p4pTd+e6hh80qqyEiHF5k+SZ3d2FXU+pQ8p9hSRdAsVU/PvWrYU5Jrs55QN3XlKrFrieIV9U81+X+V19x8PrpqqLpMTdACXbyufyCOOAitI1PukgxUAHEMMvevo0Tm3YqtyVjehGV/sdFokcPHCeXB971CMncZBjEIbyQkd5PyafoX8OFb+JEaqE2PuJkpoKD+WB7zgFQLOOZiFwCoadGhP2x90cEPCDQEXg49KNzcx1FEAA4w4BNo2q3Ehs2C8KvbIrT6vgf8c7Kf0WRB2d3O4G5uXTpzdKmZ8xzbJBS/cKNL/VIwYq29Fj/HxXx3hRdvYlte2dYlx1binYJ6qP7BaErLHn2wFh4Z58TuleRzLNYnzNzpqhZT5L7svEjbFtufQ3a3+1GeuVWv5DMEeJm1+x3aV3AdVTLGnQI94EhfVWcuWglwpMo3a0B2UpFCMLHaSAoNW7CeQ58ocWjWF1qBDqzIu0KVWMlqyzT2RTIN9iWmq3ihGvm/sJ3Y4KmayjVeIG3IqG8SoqaSEp0HsnGTFrPg7x0LFTO7xqtsLnb/U4YLq4ay3+CgPRyR2Rs6V9asy6BECfdL0hRcXXZliaBYLorc69ggvvi1chjqkeuiQ+ln4q34W9p4/GA/q09cpEkm+1XEXzxTMwTt+usPk9SbqdBJGHv/4qRVOc9iPdlI5dAir2TrMxPdqcVffsPlBzOm/QpL+zlXn/3pZWvamvMG5z3PCRlZ7qgZPyTRpD7l9Uf0k286l6zHas/64Vo09afVdKBd5DKdsfpd2FVCY6kOqPQV6xFM0fd1VbCnIlSjTqA09DMSmYjGbXDVNoBEesTKRxU5b3wpSvIrKpBJf2MZY3auQY7XgseEiz40AWze46NPHj7lCQEvH377d94pjHOILQIOH6nPnx2eAYkyzWKttCzed04dwp/XCl2fRXKOy5MIui2CPvNDTsTr+Yr1Uny390ZeaoTTukaxuzIg+tseTp9j+JzFSfS6YrAi6oPQjJRgfb845zWTezBGqcwhbR37JWtTeAyaKZ+MumSYx93wm9RfJ05esaePYCCu9IWB/8ZOIkL/rWLpoYaTzkra9Z/2xUhnPFTk+Q9BpC7uQ2Rdn2Pxu7SqlD7n2lELT47nElpL1BK8MmUZt6K7PELp5YuYcZcV43jBnAPaumnbbDpzTfvEKUh9tybbFBMfF+ZGO5iKNbJIldm7JSglctFjhYJC5R9BKsw3liY7mgq80d7SsZLPd5YlipxullwRosk2BfiAHjy6g67bUKN5jKIk9/dsK/0X6lM7WtvvSuIM99sZ2IWiDR3zx02mSzePkxHPLW52znat7I3lEWweDPeKeg/nsOauWjYsuczehuYArzbxX7akazCqGWra95zkKHb6PMG09aY3yB5OZ9jVp8wewq8k+eLBy7CmH5qy5IFNPdCFVplEbevDp06dB46FAgoWVDC5kIeAE4lTdh4ycWO1wvsLeMDrCXtoHgYYvd/t+lcZppG4JZzCwsNgQMAR2hIDGNxPVY8XOYVHMjSLOSrx/f1Ji1WebGHMWgb3K8ffPXab9fEZAeC3G/RowVx94msQ1J3yWk5sSrjk8acqywc/oWmotBKQjfIrVfAbxS5pnVG+3dpXahxwd1qCZw7+vbqpMqjdqQynOMspmQm0FEW6c21ZBwokXnokorCBxkWz2bynNyjMOOcKzaho76sqyYAgYAteEgMY4j8DfKf5RBzfQrDo0c8I19XVPfTHcz9rwNscKGtckni5xw8XTvA8qM2dZQOw5SEe79BnMrvZsNW3Zpmxo0lluk1t+JoEWr2Qsl8IoGAKGwJ4Q0LzASs1jHcwPdoO8knIM95WANjaGgCFwaAS2cJZtBenQJmPCGwKGgCFgCBgChoAhcDsIbOEs2wrS7diX9dQQMAQMAUPAEDAEDIFDI/D/kCHo0SqoTsoAAAAASUVORK5CYII=\n",
      "text/latex": "$\\displaystyle - D^{2} + t^{2} v_{x a}^{2} - 2 t^{2} v_{x a} v_{x b} + t^{2} v_{x b}^{2} + t^{2} v_{y a}^{2} - 2 t^{2} v_{y a} v_{y b} + t^{2} v_{y b}^{2} - 2 t t_{1} v_{x a}^{2} + 2 t t_{1} v_{x a} v_{x b} - 2 t t_{1} v_{y a}^{2} + 2 t t_{1} v_{y a} v_{y b} + 2 t t_{2} v_{x a} v_{x b} - 2 t t_{2} v_{x b}^{2} + 2 t t_{2} v_{y a} v_{y b} - 2 t t_{2} v_{y b}^{2} + 2 t v_{x a} x_{a} - 2 t v_{x a} x_{b} - 2 t v_{x b} x_{a} + 2 t v_{x b} x_{b} + 2 t v_{y a} y_{a} - 2 t v_{y a} y_{b} - 2 t v_{y b} y_{a} + 2 t v_{y b} y_{b} + t_{1}^{2} v_{x a}^{2} + t_{1}^{2} v_{y a}^{2} - 2 t_{1} t_{2} v_{x a} v_{x b} - 2 t_{1} t_{2} v_{y a} v_{y b} - 2 t_{1} v_{x a} x_{a} + 2 t_{1} v_{x a} x_{b} - 2 t_{1} v_{y a} y_{a} + 2 t_{1} v_{y a} y_{b} + t_{2}^{2} v_{x b}^{2} + t_{2}^{2} v_{y b}^{2} + 2 t_{2} v_{x b} x_{a} - 2 t_{2} v_{x b} x_{b} + 2 t_{2} v_{y b} y_{a} - 2 t_{2} v_{y b} y_{b} + x_{a}^{2} - 2 x_{a} x_{b} + x_{b}^{2} + y_{a}^{2} - 2 y_{a} y_{b} + y_{b}^{2}$"
     },
     "metadata": {}
    }
   ],
   "source": [
    "p2 = expand(p1)\n",
    "display(p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   2    2 ⎛    2                       2        2                        2⎞   \n- D  + t ⋅⎝vₓ ₐ  - 2⋅vₓ ₐ⋅v_x_b + v_x_b  + v_y_a  - 2⋅v_y_a⋅v_y_b + v_y_b ⎠ + \n\n  ⎛           2                               2                               \nt⋅⎝- 2⋅t₁⋅vₓ ₐ  + 2⋅t₁⋅vₓ ₐ⋅v_x_b - 2⋅t₁⋅v_y_a  + 2⋅t₁⋅v_y_a⋅v_y_b + 2⋅t₂⋅vₓ ₐ\n\n                   2                                2                         \n⋅v_x_b - 2⋅t₂⋅v_x_b  + 2⋅t₂⋅v_y_a⋅v_y_b - 2⋅t₂⋅v_y_b  + 2⋅vₓ ₐ⋅xₐ - 2⋅vₓ ₐ⋅x_b\n\n                                                                              \n - 2⋅v_x_b⋅xₐ + 2⋅v_x_b⋅x_b + 2⋅v_y_a⋅yₐ - 2⋅v_y_a⋅y_b - 2⋅v_y_b⋅yₐ + 2⋅v_y_b⋅\n\n   ⎞     2     2     2      2                                                 \ny_b⎠ + t₁ ⋅vₓ ₐ  + t₁ ⋅v_y_a  - 2⋅t₁⋅t₂⋅vₓ ₐ⋅v_x_b - 2⋅t₁⋅t₂⋅v_y_a⋅v_y_b - 2⋅t\n\n                                                               2      2     2 \n₁⋅vₓ ₐ⋅xₐ + 2⋅t₁⋅vₓ ₐ⋅x_b - 2⋅t₁⋅v_y_a⋅yₐ + 2⋅t₁⋅v_y_a⋅y_b + t₂ ⋅v_x_b  + t₂ ⋅\n\n     2                                                                       2\nv_y_b  + 2⋅t₂⋅v_x_b⋅xₐ - 2⋅t₂⋅v_x_b⋅x_b + 2⋅t₂⋅v_y_b⋅yₐ - 2⋅t₂⋅v_y_b⋅y_b + xₐ \n\n                 2     2                 2\n - 2⋅xₐ⋅x_b + x_b  + yₐ  - 2⋅yₐ⋅y_b + y_b ",
      "image/png": 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\n",
      "text/latex": "$\\displaystyle - D^{2} + t^{2} \\left(v_{x a}^{2} - 2 v_{x a} v_{x b} + v_{x b}^{2} + v_{y a}^{2} - 2 v_{y a} v_{y b} + v_{y b}^{2}\\right) + t \\left(- 2 t_{1} v_{x a}^{2} + 2 t_{1} v_{x a} v_{x b} - 2 t_{1} v_{y a}^{2} + 2 t_{1} v_{y a} v_{y b} + 2 t_{2} v_{x a} v_{x b} - 2 t_{2} v_{x b}^{2} + 2 t_{2} v_{y a} v_{y b} - 2 t_{2} v_{y b}^{2} + 2 v_{x a} x_{a} - 2 v_{x a} x_{b} - 2 v_{x b} x_{a} + 2 v_{x b} x_{b} + 2 v_{y a} y_{a} - 2 v_{y a} y_{b} - 2 v_{y b} y_{a} + 2 v_{y b} y_{b}\\right) + t_{1}^{2} v_{x a}^{2} + t_{1}^{2} v_{y a}^{2} - 2 t_{1} t_{2} v_{x a} v_{x b} - 2 t_{1} t_{2} v_{y a} v_{y b} - 2 t_{1} v_{x a} x_{a} + 2 t_{1} v_{x a} x_{b} - 2 t_{1} v_{y a} y_{a} + 2 t_{1} v_{y a} y_{b} + t_{2}^{2} v_{x b}^{2} + t_{2}^{2} v_{y b}^{2} + 2 t_{2} v_{x b} x_{a} - 2 t_{2} v_{x b} x_{b} + 2 t_{2} v_{y b} y_{a} - 2 t_{2} v_{y b} y_{b} + x_{a}^{2} - 2 x_{a} x_{b} + x_{b}^{2} + y_{a}^{2} - 2 y_{a} y_{b} + y_{b}^{2}$"
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "source": [
    "(p2.coeff(t**2))*t**2 + (p2.coeff(t))*t + (p2.coeff(t,n=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "    2                       2        2                        2\nvₓ ₐ  - 2⋅vₓ ₐ⋅v_x_b + v_x_b  + v_y_a  - 2⋅v_y_a⋅v_y_b + v_y_b ",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle v_{x a}^{2} - 2 v_{x a} v_{x b} + v_{x b}^{2} + v_{y a}^{2} - 2 v_{y a} v_{y b} + v_{y b}^{2}$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "           2                               2                                  \n- 2⋅t₁⋅vₓ ₐ  + 2⋅t₁⋅vₓ ₐ⋅v_x_b - 2⋅t₁⋅v_y_a  + 2⋅t₁⋅v_y_a⋅v_y_b + 2⋅t₂⋅vₓ ₐ⋅v_\n\n                2                                2                            \nx_b - 2⋅t₂⋅v_x_b  + 2⋅t₂⋅v_y_a⋅v_y_b - 2⋅t₂⋅v_y_b  + 2⋅vₓ ₐ⋅xₐ - 2⋅vₓ ₐ⋅x_b - \n\n                                                                              \n2⋅v_x_b⋅xₐ + 2⋅v_x_b⋅x_b + 2⋅v_y_a⋅yₐ - 2⋅v_y_a⋅y_b - 2⋅v_y_b⋅yₐ + 2⋅v_y_b⋅y_b",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle - 2 t_{1} v_{x a}^{2} + 2 t_{1} v_{x a} v_{x b} - 2 t_{1} v_{y a}^{2} + 2 t_{1} v_{y a} v_{y b} + 2 t_{2} v_{x a} v_{x b} - 2 t_{2} v_{x b}^{2} + 2 t_{2} v_{y a} v_{y b} - 2 t_{2} v_{y b}^{2} + 2 v_{x a} x_{a} - 2 v_{x a} x_{b} - 2 v_{x b} x_{a} + 2 v_{x b} x_{b} + 2 v_{y a} y_{a} - 2 v_{y a} y_{b} - 2 v_{y b} y_{a} + 2 v_{y b} y_{b}$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "   2     2     2     2      2                                                 \n- D  + t₁ ⋅vₓ ₐ  + t₁ ⋅v_y_a  - 2⋅t₁⋅t₂⋅vₓ ₐ⋅v_x_b - 2⋅t₁⋅t₂⋅v_y_a⋅v_y_b - 2⋅t\n\n                                                               2      2     2 \n₁⋅vₓ ₐ⋅xₐ + 2⋅t₁⋅vₓ ₐ⋅x_b - 2⋅t₁⋅v_y_a⋅yₐ + 2⋅t₁⋅v_y_a⋅y_b + t₂ ⋅v_x_b  + t₂ ⋅\n\n     2                                                                       2\nv_y_b  + 2⋅t₂⋅v_x_b⋅xₐ - 2⋅t₂⋅v_x_b⋅x_b + 2⋅t₂⋅v_y_b⋅yₐ - 2⋅t₂⋅v_y_b⋅y_b + xₐ \n\n                 2     2                 2\n - 2⋅xₐ⋅x_b + x_b  + yₐ  - 2⋅yₐ⋅y_b + y_b ",
      "image/png": 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\n",
      "text/latex": "$\\displaystyle - D^{2} + t_{1}^{2} v_{x a}^{2} + t_{1}^{2} v_{y a}^{2} - 2 t_{1} t_{2} v_{x a} v_{x b} - 2 t_{1} t_{2} v_{y a} v_{y b} - 2 t_{1} v_{x a} x_{a} + 2 t_{1} v_{x a} x_{b} - 2 t_{1} v_{y a} y_{a} + 2 t_{1} v_{y a} y_{b} + t_{2}^{2} v_{x b}^{2} + t_{2}^{2} v_{y b}^{2} + 2 t_{2} v_{x b} x_{a} - 2 t_{2} v_{x b} x_{b} + 2 t_{2} v_{y b} y_{a} - 2 t_{2} v_{y b} y_{b} + x_{a}^{2} - 2 x_{a} x_{b} + x_{b}^{2} + y_{a}^{2} - 2 y_{a} y_{b} + y_{b}^{2}$"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "b= -2*t_1*v_x_a**2 + 2*t_1*v_x_a*v_x_b - 2*t_1*v_y_a**2 + 2*t_1*v_y_a*v_y_b + 2*t_2*v_x_a*v_x_b - 2*t_2*v_x_b**2 + 2*t_2*v_y_a*v_y_b - 2*t_2*v_y_b**2 + 2*v_x_a*x_a - 2*v_x_a*x_b - 2*v_x_b*x_a + 2*v_x_b*x_b + 2*v_y_a*y_a - 2*v_y_a*y_b - 2*v_y_b*y_a + 2*v_y_b*y_b\nc= -D**2 + t_1**2*v_x_a**2 + t_1**2*v_y_a**2 - 2*t_1*t_2*v_x_a*v_x_b - 2*t_1*t_2*v_y_a*v_y_b - 2*t_1*v_x_a*x_a + 2*t_1*v_x_a*x_b - 2*t_1*v_y_a*y_a + 2*t_1*v_y_a*y_b + t_2**2*v_x_b**2 + t_2**2*v_y_b**2 + 2*t_2*v_x_b*x_a - 2*t_2*v_x_b*x_b + 2*t_2*v_y_b*y_a - 2*t_2*v_y_b*y_b + x_a**2 - 2*x_a*x_b + x_b**2 + y_a**2 - 2*y_a*y_b + y_b**2\n"
    }
   ],
   "source": [
    "a = p2.coeff(t**2)\n",
    "b = p2.coeff(t)\n",
    "c = p2.coeff(t,n=0)\n",
    "display(a); display(b); display(c)\n",
    "print(\"b=\",b)\n",
    "print(\"c=\",c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "    2        2\nvₓ ₐ  + v_y_a ",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle v_{x a}^{2} + v_{y a}^{2}$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "           2             2                         \n- 2⋅t₁⋅vₓ ₐ  - 2⋅t₁⋅v_y_a  + 2⋅vₓ ₐ⋅xₐ + 2⋅v_y_a⋅yₐ",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle - 2 t_{1} v_{x a}^{2} - 2 t_{1} v_{y a}^{2} + 2 v_{x a} x_{a} + 2 v_{y a} y_{a}$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "   2     2     2     2      2                                    2     2\n- D  + t₁ ⋅vₓ ₐ  + t₁ ⋅v_y_a  - 2⋅t₁⋅vₓ ₐ⋅xₐ - 2⋅t₁⋅v_y_a⋅yₐ + xₐ  + yₐ ",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle - D^{2} + t_{1}^{2} v_{x a}^{2} + t_{1}^{2} v_{y a}^{2} - 2 t_{1} v_{x a} x_{a} - 2 t_{1} v_{y a} y_{a} + x_{a}^{2} + y_{a}^{2}$"
     },
     "metadata": {}
    }
   ],
   "source": [
    "p3 = expand(x1**2 + y1**2 - D**2)\n",
    "a = p3.coeff(t**2)\n",
    "b = p3.coeff(t)\n",
    "c = p3.coeff(t,n=0)\n",
    "display(a); display(b); display(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}